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Abstract:

A method for warming up a first instrument that includes providing an
instrument measuring a first instrument temperature with the first
temperature sensor at a starting time; measuring a first air temperature
with the second temperature sensor at the starting time; determining a
first profile based at least in part on the first instrument temperature
and the first air temperature, the first profile representing an amount
of first electrical current applied as a function of time, the first
profile selected to provide a predicted level of instrument performance
within a warm-up time; applying the first electrical current according to
the first profile; and providing an operator at the starting time with a
numerical value for the warm-up time of the instrument, wherein the
warm-up time is based at least in part on the first instrument
temperature and the first air temperature.

Claims:

1. A method for warming up a first instrument, the method comprising
steps of: providing an instrument including a light source configured to
emit a beam of light, a beam steering device configured to direct the
beam of light in a first direction, the first direction based on rotation
of the beam steering device about a first axis and a second axis, a
distance meter configured to measure a distance traveled by the beam of
light from the instrument to a point on an object, a first temperature
sensor configured to measure an instrument temperature at a first
position in the instrument, a second temperature sensor configured to
measure an air temperature, a first heat source configured to inject heat
into the instrument in response to an application of a first electrical
current, and a processor configured to control the first electrical
current as a function of time; measuring a first instrument temperature
with the first temperature sensor at a starting time; measuring a first
air temperature with the second temperature sensor at the starting time;
determining a first profile based at least in part on the first
instrument temperature and the first air temperature, the first profile
representing an amount of first electrical current applied as a function
of time, the first profile selected to provide a predicted level of
instrument performance within a warm-up time; applying the first
electrical current according to the first profile; and providing an
operator at the starting time with a numerical value for the warm-up time
of the instrument, wherein the warm-up time is based at least in part on
the first instrument temperature and the first air temperature.

2. The method of claim 1, wherein, in the step of providing an
instrument, the first heat source is a first motor.

3. The method of claim 1, wherein the step of determining a first profile
further includes determining a rapid-heating part and a relaxation part
of the first profile, the rapid-heating part representing a relatively
rapid application of current to the first heat source so as to relatively
rapidly increase the average temperature of the instrument and the
relaxation part representing a relatively lower application of current so
as to permit the instrument to more nearly approach a thermal equilibrium
throughout the volume of the instrument.

4. The method of claim 1, wherein the step of providing an instrument
further includes a step of providing a third temperature sensor
configured to measure an instrument temperature at a second location in
the instrument.

5. The method of claim 4, wherein the step of determining the first
profile is further based on the temperature measured by the third
temperature sensor at the starting time.

6. The method of claim 2, wherein the step of providing an instrument
further includes providing a second heat source, the second heat source
being a second motor.

7. The method of claim 6, further including a step of determining a
second profile, the second profile based at least in part on the first
instrument temperature and the first air temperature, the second profile
representing an amount of second electrical current applied as a function
of time to the second heat source, the second profile selected to provide
a predicted level of instrument performance within the warm-up time.

8. The method of claim 1, wherein, in the step of providing an
instrument, the beam steering device further includes a first structure,
a second structure, a first motor, and a second motor, wherein the first
motor is configured to rotate the first structure about a first axis and
the second motor is configured to rotate the second structure about a
second axis.

9. The method of claim 8, wherein the step of providing an instrument
further includes a step of providing a first angle sensor and a second
angle sensor, the first angle sensor configured to measure a first angle
of rotation about the first axis and the second angle sensor configured
to measure a second angle of rotation about the second axis.

10. The method of claim 1, further including a step of determining a
heating model for the instrument, the heating model based at least in
part on data collected from a sequence of measurements on a reference
device, the reference device being a device substantially similar to the
instrument, wherein the step of determining the first profile is further
based at least in part on the heating model.

11. The method of claim 1, further including a step of giving the
operator an indication of time remaining before warm-up is complete.

12. The method of claim 1, further including a step of automatically
turning on the instrument at a second time, the second time selected to
make the instrument ready for operation at a third time, the difference
in the third time and the second time equal to the determined warm-up
time.

[0002] The present invention relates to instrument warm-up and stability,
and more particularly to systems and methods for automatically warming up
instruments such as laser trackers or for checking the stability of such
instruments.

BACKGROUND

[0003] There is a class of instrument that measures the coordinates of a
point by sending a laser beam to the point. The laser beam may impinge
directly on the point or may impinge on a retroreflector target that is
in contact with the point. In either case, the instrument determines the
coordinates of the point by measuring the distance and the two angles to
the target. The distance is measured with a distance-measuring device
such as an absolute distance meter or an interferometer. The angles are
measured with an angle-measuring device such as an angular encoder. A
gimbaled beam-steering mechanism within the instrument directs the laser
beam to the point of interest. Exemplary systems for determining
coordinates of a point are described by U.S. Pat. No. 4,790,651 to Brown
et al. and U.S. Pat. No. 4,714,339 to Lau et al.

[0004] The laser tracker is a particular type of coordinate-measuring
device that tracks the retroreflector target with one or more laser beams
it emits. A device that is closely related to the laser tracker is the
laser scanner. The laser scanner steps one or more laser beams to points
on a diffuse surface. The laser tracker and laser scanner are both
coordinate-measuring devices. An exemplary laser scanner is described in
U.S. Pat. No. 7,430,068 to Becker et al. It is common practice today to
use the term laser tracker to also refer to laser scanner devices having
distance- and angle-measuring capability. There is also a hybrid category
of instruments known as total stations or tachymeters that may measure a
retroreflector or a point of a diffusely scattering surface. An exemplary
total station is described in U.S. Pat. No. 4,346,989 to Gort et al.
Laser trackers, which typically have accuracies from a few micrometers to
a few tens of micrometers, are usually much more accurate than total
stations or scanners. The broad definition of laser tracker, which
includes laser scanners and total stations, is used throughout this
application.

[0005] Ordinarily the laser tracker sends a laser beam to a retroreflector
target. A common type of retroreflector target is the spherically mounted
retroreflector (SMR), which comprises a cube-corner retroreflector
embedded within a metal sphere. The cube-corner retroreflector comprises
three mutually perpendicular mirrors. The vertex, which is the common
point of intersection of the three mirrors, is located at the center of
the sphere. Because of this placement of the cube corner within the
sphere, the perpendicular distance from the vertex to any surface on
which the SMR rests remains constant, even as the SMR is rotated.
Consequently, the laser tracker can measure the 3D coordinates of a
surface by following the position of an SMR as it is moved over the
surface. Stating this another way, the laser tracker needs to measure
only three degrees of freedom (one radial distance and two angles) to
fully characterize the 3D coordinates of a surface.

[0006] Compensation parameters are numerical values that are stored in
software or firmware accessible to the tracker. These numerical values
are applied to raw tracker data to improve tracker accuracy. Initially,
the manufacturer of the tracker finds the compensation parameters by
performing measurements called compensation procedures. Later, the
tracker will be used at the customer's site to make measurements.
Periodically, the tracker will be checked for accuracy by performing
interim tests. If the accuracy is substandard, the tracker operator will
perform one or more compensation procedures on the factory floor. These
can take from a few minutes to an hour or more, depending on the
particular tracker and on the tests that are required. In most cases, the
main cause of reduced tracker accuracy is thermal drift, although
mechanical shock can also be important.

[0007] Compensation parameters generally relate to physical
characteristics of the instrument. In examples given hereinbelow, some of
these compensation parameters relate to (1) offset of a laser beam with
respect to a mechanical point of rotation (gimbal point), (2) angle of a
laser beam with respect to a line drawn perpendicular to two mechanical
axes, and (3) non-squareness of two mechanical axes. Many other types of
compensation parameters are used, but generally these compensation
parameters (also called kinematic model parameters or simply parameters)
relate to physical characteristics of the instrument.

[0008] Each laser tracker compensation parameter has a true value, which
typically fluctuates with time as a result of temperature changes and
mechanical disturbances such as shock. The true value is typically known
only imperfectly. In addition, each laser tracker compensation parameter
has a recorded value, which is a particular constant number. The recorded
value is used to correct raw laser tracker measurements by means of a
particular mathematical formula. In general, the recorded value and the
true value are not equal.

[0009] When a laser tracker is powered on after having been off for a
significant time, it warms up as a result of the heat produced by the
motors and the internal electronics. After a period of time, typically on
the order of an hour or two, the tracker reaches a stable equilibrium
temperature, if the ambient temperature is stable. After warm-up is
complete, standard metrology practice calls for compensating the
instrument, followed by an interim test procedure to verify that the
compensation was successful. After the compensation and the interim test
have been completed, the tracker is ready to take measurements with
optimum accuracy.

[0010] If the compensation procedure is performed before the tracker has
fully warmed up, the true values of the compensation parameters will
continue to change as the tracker continues to warm up, while the
recorded values of the compensation parameters remain constant. This in
turn degrades the performance of the laser tracker and forces the user to
repeat the compensation and interim test procedures.

[0011] From the tracker user's point of view, the time taken for warm-up,
compensation, and interim testing represents lost time, because the
tracker is not available to take measurements. For this reason, it is
standard metrology practice to keep the tracker powered on continuously
whenever possible. This eliminates the warm-up period and assures that
the tracker is ready to take measurements at any time.

[0012] In many real world situations, however, it is not possible to keep
the instrument powered on continuously. For example, the instrument may
need to be stored or transported to another job site, or the user may
simply want to conserve energy. In such cases it is not possible to avoid
warm-up. In these cases, the best that one can hope for is to minimize
the amount of time lost, both for the instrument and for the user.

[0013] The warm-up scenario places the user in a difficult situation. On
the one hand, there is a need to minimize the amount of time that is lost
waiting for the instrument to warm-up. On the other hand, there is a need
for accuracy in subsequent measurements. This tradeoff is faced by laser
tracker users every time they power up their instruments.

[0014] The difficulty is exacerbated by the fact that every warm-up
sequence is different. The detailed behavior depends on the initial
temperature distribution within the tracker, the ambient conditions, and
the idiosyncrasies of the individual instrument. Also, while the long
term behavior is roughly steady state, there is an element of
subjectivity when a human operator decides whether the instrument is
"close enough" to a steady-state value. In other words, the detailed
behavior of a laser tracker during warm-up is complex, and determining
when the tracker is warmed up is a non-trivial exercise.

[0015] A serious limitation of present methods is that there is no
guarantee that the user possesses sufficient skill and knowledge to make
the warm-up determination correctly, which can lead to many errors.
Another serious limitation is that no special steps are taken to reduce
the time to complete the warm-up. With the usual application of heat
sources within the tracker, warm-up time for some types of trackers may
take up to two hours on average.

[0016] To some extent, the way the tracker is mounted may help to reduce
the required warm-up time. An example of such a way of mounting a tracker
is given in U.S. Published Patent Application No. 2010/0195117 to Easley
et al. However, this mounting method does not provide a method for
determining how long to wait before the tracker is warmed up. Also, it is
a purely passive method and therefore provides only a small improvement.

[0017] What is needed is an automated mechanism to warm-up and stabilize
the tracker as rapidly as possible, with minimal additional cost, and
with high confidence that the tracker is in a warmed up state to obtain
accurate measurements. In addition, if the instrument does not have the
expected absolute performance or stability, it is desirable to have a
method to diagnose the cause of the decreased performance or stability.
It may also be desirable to provide a "paper trail" to auditors
demonstrating that the laser tracker was warmed up or stable when used.

SUMMARY

[0018] According to an embodiment of the invention, a method for warming
up a first instrument includes steps of: providing an instrument
including a light source configured to emit a beam of light, a beam
steering device configured to direct the beam of light in a first
direction, the first direction based on rotation of the beam steering
device about a first axis and a second axis, a distance meter configured
to measure a distance traveled by the beam of light from the instrument
to a point on an object, a first temperature sensor configured to measure
an instrument temperature at a first position in the instrument, a second
temperature sensor configured to measure an air temperature, a first heat
source configured to inject heat into the instrument in response to an
application of a first electrical current, and a processor configured to
control the first electrical current as a function of time. The method
also includes: measuring a first instrument temperature with the first
temperature sensor at a starting time; measuring a first air temperature
with the second temperature sensor at the starting time; determining a
first profile based at least in part on the first instrument temperature
and the first air temperature, the first profile representing an amount
of first electrical current applied as a function of time, the first
profile selected to provide a predicted level of instrument performance
within a warm-up time; applying the first electrical current according to
the first profile; and providing an operator at the starting time with a
numerical value for the warm-up time of the instrument, wherein the
warm-up time is based at least in part on the first instrument
temperature and the first air temperature.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Embodiments will now be described, by way of example only, with
reference to the accompanying drawings which are meant to be exemplary,
not limiting, and wherein like elements are numbered alike in several
figures, in which:

[0020] FIG. 1 illustrates a laser tracker in which exemplary automated
warm-up and stability embodiments may be implemented;

[0029]FIG. 13 shows a flowchart of a method for minimizing the time
required to warm-up an instrument.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0030] FIG. 1 illustrates a laser tracker 10 in which exemplary automated
warm-up and stability embodiments may be implemented. The laser tracker
10 sends a light beam 46 from the laser tracker 10 to SMR 26, which
returns the light beam 48 to tracker 10. Light beam 48 is slightly
reduced in optical power with respect to light beam 46 but otherwise is
nearly identical to light beam 46. An exemplary gimbaled beam-steering
mechanism 12 of laser tracker 10 includes a first structure 14 mounted on
a base 16. The first structure 14 is rotated about a first (azimuth) axis
20. A second structure 15 is mounted on the first structure 14 and is
rotated about a second (zenith) axis 18. The second axis 18 and the first
axis 20 intersect orthogonally, internally to tracker 10, at gimbal point
22, which is typically the origin for distance measurements. The light
beam 46 virtually passes through gimbal point 22 and is pointed
orthogonal to second axis 18. In other words, the path of light beam 46
is in the plane normal to second axis 18. Light beam 46 is pointed in the
desired direction by rotation of second structure 15 about the second
axis 18 and rotation of first and second structures 14, 15 about the
first axis 20. A zenith angular encoder (not shown), internal to the
tracker, is attached to a zenith axle (not shown) aligned to the second
axis 18, and an azimuth angular encoder (not shown), internal to the
tracker, is attached to an azimuth axle (not shown) aligned to the first
axis 20. The angular encoders indicate, to high accuracy, the angles of
rotation of the first and second structures about the first and second
axes. A first motor 32, internal to the tracker and attached to the
azimuth axle, provides rotation of the first and second structures about
the first axis. A second motor 34, internal to the tracker and attached
to the zenith axle, provides rotation of the second structure about the
second axis. The tracker 10 measures the radial distance between gimbal
point 22 and retroreflector 26, as well as the rotation angles about the
zenith and azimuth axes 18, 20, to find the position of retroreflector 26
within the spherical coordinate system of the tracker.

[0031] In an embodiment, the second structure 15 is a payload that emits
light from elements disposed on the payload. These elements may be light
sources such as lasers or superluminescent diodes that are located on the
payload and that emit light into free space. Alternatively, these
elements may be optical fibers that are connected to light sources, the
ends of the optical fibers launching the light into free space within the
payload. The light sources may be located in the second structure
(payload) 15, the first structure 14, or the base 16. In another
embodiment, the second structure is a mirror that steers light emanating
from the base 16 or the first structure 14 out of the tracker 10 as the
light beam 46.

[0032] Frontsight mode is defined as the ordinary mode of operation of the
tracker. Backsight mode is obtained by starting in frontsight mode and
then doing the following: (1) rotating the azimuth axis by 180 degrees;
(2) rotating the zenith axis to have the negative of the original zenith
angle (where the direction of the azimuth axis 20 corresponds to a zenith
angle of zero); and (3) turning on tracking. The last step will cause the
light beam to move to the proper position on the cube-corner or mirror so
that the light beam 48 retraces the path of light beam 46. In an ideal
laser tracker, the measured three-dimensional coordinates of a
retroreflector or mirror target in frontsight mode and backsight mode are
the same. In a real tracker, these measured angles are not exactly the
same, and the discrepancy is an indicator of the quality of measurement
of the tracker. The two-face measurement is particularly sensitive to
parameter errors, discussed in more detail hereinbelow and hence provides
an effective test for quickly evaluating a laser tracker.

[0033] In the two-face measurement, an (x, y, z) value is obtained in
frontsight mode and an (x, y, z) value is obtained in backsight mode.
Here x, y, and z are coordinates within the fixed frame of reference
within which the laser tracker sits. It is customary in two-face
measurements to set the radial distance to be the same value for
frontsight and backsight modes. As a result, the difference in the
frontsight and backsight coordinate readings is entirely along the
transverse direction. Here transverse direction is defined as the
direction perpendicular to the light beam from the tracker. The two-face
difference, also known as the two-face error, is the transverse distance
between readings obtained in frontsight and backsight modes. In this
measurement, the two-face error of interest is the uncompensated two-face
error, in other words, the two-face error before compensation parameters
have been applied. The purpose of the compensation parameters to improve
measurement accuracy, and hence the application of compensation
parameters usually reduces the two-face error. In other words, the
compensated two-face error is usually less than the uncompensated
two-face error.

[0034] The reason two-face measurements are particularly effective at
indicating tracker problems is that they are sensitive to many of the
typical error modes within a laser tracker. In an ideal tracker the light
beam passes, at least virtually, through the tracker gimbal point. In a
real tracker, the light beam is offset with respect to the gimbal point.
This offset gives rise to two parameters--TX and TY--which are simply the
offset distances in the X and Y directions at the line of closest
approach to the gimbal point. Here the X and Y directions are taken with
respect to payload 15 of FIG. 1. (These differ from the x and y
directions, which are taken with respect to the fixed frame of reference
within which the laser tracker sits.) As long as these parameters are
stable and are known accurately, then the offset in the light beam with
respect to the gimbal point will not cause an error. However, if the
offset changes with temperature, for example as the tracker warms up,
then the true values of TX and TY also change. The two-face measurement
is very sensitive to TX and TY errors.

[0035] In an ideal tracker, when the zenith angle is set to ninety
degrees, the light beam is perpendicular to the azimuth mechanical axis
and zenith mechanical axis. In a real tracker, the light beam departs
slightly from perpendicularity. This tilt in the light beam gives rise to
two parameters--RX and RY--which are simply the angular tilts about the X
and Y directions. As long as these parameters are stable and are known
accurately, then the tilt in the light beam with respect to the
mechanical axes will not cause an error. However, if the offset changes
with temperature, for example as the tracker warms up, then the true
values of RX and RY change. The two-face measurement is sensitive to RX
and RY errors.

[0036] The methods for finding parameters TX, TY, RX, RY for the type of
tracker shown in FIG. 1 are described in U.S. Pat. No. 7,327,446 ('446)
to Cramer et al., incorporated by reference herein. Other formulas will
be applicable to laser trackers that use other beam steering methods. For
example, some laser trackers use a mirror to steer the light beam, and
these trackers have different parameters than the tracker shown in FIG.
1. However, two-face tests are used to identify problems and find
parameters for all types of trackers regardless of the beam steering
mechanism.

[0037] Two-face errors may also reflect other types of tracker errors. For
example, it can be sensitive to many types of errors seen in the angular
encoders. Under some conditions, it is also sensitive to axis
non-squareness errors.

[0038] If the tracker is stable, then the two-face measurement can be used
as part of a compensation procedure to find the correct parameter values.
If the tracker is not stable, then the variability in the two-face
measurement values can be used to identify this lack of stability. The
particular parameters values and how these values change in time can be
used as a diagnostic tool to assist the user or service representative in
finding the physical cause of any problem that may occur. This is one of
the reasons that the exemplary methods described herein are useful for
checking the stability of a tracker that is already warmed up as well as
a tracker that is in the warm-up phase.

[0039] Exemplary embodiments described hereinbelow are for methods to
quickly ensure consistent warm-up of trackers. Exemplary embodiments can
include performing repeated two-face measurements (i.e., frontsight and
backsight measurements) on a single retroreflector target, which might be
located either on a tracker (i.e., an on-tracker target, for example, as
described in the '446 patent) or at an arbitrary point in the volume
surrounding the tracker. If the point is located off the tracker, the
retroreflector can be placed in a nest, which might be attached, for
example, to a floor, instrument stand, or structure. These measurements
can be made at regular intervals, which might be closely spaced in time.
After each two-face measurement is performed, the two-face error, defined
as the difference in the readings of the frontsight and backsight modes,
is calculated. The two-face readings are used to decide whether the
tracker is stable. Ways of doing this are discussed hereinbelow.

[0040] In another exemplary embodiment, a second target can be added in a
manner that separates translational errors (for example, TX and TY
errors) and angular errors (for example, RX and RY errors). There are
several ways to separate translational and angular errors in the tracker.
The first way is to place two different retroreflector targets at
different distances. Distant targets are more susceptible to the effects
of angular errors than are nearby targets, while distant and nearby
targets are equally affected by translational errors. Because of this,
two-face measurements can be made on two retroreflector targets placed at
two different ranges. The readings from these measurements can be used to
separate the two types of errors.

[0041] A second way of separating translational and angular errors is to
select a retroreflector as the first target and a mirror as the second
target. The mirror responds most strongly to angular errors in the
tracker, while the retroreflector responds to both angular and
translational errors. The method for separating translational and angular
errors using retroreflector and mirror targets is explained in detail in
the '446 patent. The criterion for deciding when a tracker is warmed up
is based on delta values of two-face measurements for the two different
targets. A variety of specific mathematical rules may be used to decide
when a tracker has warmed up, as is described below.

[0042] In yet another exemplary embodiment, parameters are calculated from
the two-face measurements. Some parameters (for example, RX and RY for
some types of trackers) may be collected using mirror targets alone.
Other types of parameters (for example, TX and TY for some other types of
trackers) are collected using two or more retroreflector or mirror
targets. The relevant parameters differ according to the specific
tracker. For example, parameters are different for a type of tracker that
uses a steering mirror to direct the light beam out of the tracker than
for the type of tracker shown in FIG. 1. In general, any parameters for
any type of tracker may be used in a mathematical rule that indicates
when a tracker is warmed up or stable.

[0043] In one or more exemplary embodiments, the tracker 10 can include a
user interface that would tell the user the error of the tracker 10
relative to the maximum permissible error (MPE) for that particular
target point if the user were to start using the tracker at any
particular moment. MPE is a specification that tracker manufacturers
publish, which indicate tracker accuracy as a function of range.

[0044]FIG. 2 illustrates a plot of uncompensated two-face error on the
vertical axis versus time on the horizontal axis. The plot illustrates
that, as the tracker 10 warms up, it at first has an initial
uncompensated two-face error value 215. As it warms up, the two-face
error changes rapidly in a transient phase 210. The uncompensated
two-face error may be positive or negative, and it may become larger or
smaller as the tracker warms up. As time passes, the tracker 10 enters a
plateau phase 220 in which the two-face error approaches a plateau value
225, which might also be called a steady-state value. As the tracker 10
nears the plateau value, it is considered stable and ready to be
compensated.

[0045]FIG. 10 shows a flowchart for a first exemplary embodiment for a
method 1000 of determining whether an instrument such as a laser tracker
is warmed up or stable. At least one target, which may be a
retroreflector or mirror, is needed. The method of using retroreflectors
or mirrors to perform two-face measurements is described in more detail
in the '446 patent. Additional targets, which may be any combination of
retroreflectors or mirrors, may be used. The procedure includes steps
1010, 1020, 1030, 1040, 1050, and 1060. Step 1010 is to make a
measurement of each target in frontsight mode. Step 1020 is to make a
measurement of each target in backsight mode. The order of taking
frontsight and backsight measurements is not important, but the total
time to complete the test should be minimized to mitigate drift effects.
Step 1030 is to calculate the two-face error for each of the targets. The
two-face error value is a transverse distance and has units of length.
Step 1040 is to decide whether the targets have been measured for the
first time. If so, a second set of measurements are made, beginning again
with step 1010. If not, the procedure continues to step 1050, where one
or more stability metrics are calculated.

[0046] A stability metric is any value defined by a rule that decides if
the tracker is stable. The stability metric may be a simple number based
on a pair of measured two-face errors, or it may be a more complicated
value based on several measurements combined according to a mathematical
rule. An example of the latter case of a relatively complicated value
based on several parameters and on manufacturer's specifications is given
hereinbelow with reference to FIG. 10. The stability metric may depend on
a series of measured values from the past (for example, a moving average
or some other type of filtered value) or simply on the most recently
collected measured values. Step 1060 is to decide whether the stability
metrics have satisfied the termination criteria. There may be a single
termination criterion, or there may be several termination criteria. If
there are several termination criteria, then there is a corresponding
stability metric for each criterion, although some of the criteria may be
obtained without finding two-face errors. For example, one criterion
might be that the tracker compensated two-face errors meet manufacturer's
MPE specifications. This could be used in conjunction with a second
criterion related to the stability of the two-face errors over time. If
multiple termination criteria are given, then each of these must be met
by the corresponding stability metrics for the tracker to be considered
stable. If the stability metrics satisfy the termination criteria, the
tracker is considered to be stable or warmed up, and the next step can be
carried out. The next step will usually be either to perform a
compensation procedure on the tracker or to begin making measurements
with the tracker.

[0047] Probably the simplest type of stability metric is the absolute
value of the delta (difference) in the two preceding two-face errors. The
threshold condition in this case can simply be a given numerical value.
If the stability metric is less than the threshold value, the tracker is
considered to be stable. Otherwise it is not considered to be stable, and
two-face measurements are continued. Referring to FIG. 2, we see that
initially the two-face errors are changing rapidly, which means that the
delta (difference) in the two face values is large. Hence a small delta
value is indicative of a stable tracker. One complication is that, in
general, the two-face error illustrated in FIG. 2 has some noise in
addition to the smooth curve that shows the general trend. In this case,
establishing stability based on a single delta value may not provide
adequate assurance that the tracker is fully stable.

[0048] The steps of method 1000 of FIG. 10 can be conveniently described
in words rather than in flowchart format. To calculate the stability
metric, at least two two-face errors are needed. Consequently, there are
a plurality of backsight measurements, frontsight measurements, and
two-face error calculations, and there is at least one stability metric.
The frontsight and backsight measurements are alternated. If the
termination criteria are not met, any number of repeated two-face
measurements may be required before the tracker is regarded as stable.

[0049]FIG. 3 illustrates a flowchart for a second exemplary embodiment
for a method 300 of determining whether an instrument such as a laser
tracker is warmed up or stable. The method 300 includes steps 310, 320,
330, 340, and 350. Step 310 is to make two-face measurements on at least
two targets, which may be retroreflector or mirror targets. Step 310 may
also optionally include measurements in addition to two-face
measurements. Step 320 is to calculate instrument compensation
parameters, generally a subset of parameters rather than a complete set
of instrument parameters. The measurements performed in step 310 provide
sufficient information to calculate at least some parameters of the
instrument. Step 330 is to check whether the measurements of step 310
were performed for the first time. If so, they are performed again,
starting with step 310. If not, step 340 is carried out to calculate a
stability metric. Step 350 is to check whether the stability metric is
less than the threshold value. If so, the instrument is considered to be
stable or warmed up. Otherwise, additional measurements and calculations,
beginning with step 310, are repeated iteratively.

[0050] The method 300 as described with respect to FIG. 3 is an overall
method for which further exemplary embodiments are now described.

[0051]FIG. 4 illustrates a method 400 in accordance with exemplary
embodiments. The method 400 includes steps 410, 420, 430, 440, and 450.
Step 410 is to perform a compensation procedure. For the exemplary laser
tracker shown in FIG. 1 and described more fully in the '446 patent, a
convenient compensation procedure is a self-compensation procedure in
which two on-tracker targets, an on-tracker retroreflector and an
on-tracker mirror, are used in an fully automated tracker procedure to
find tracker parameters. This procedure takes about 4 to 5 minutes to
carry out. Other compensation procedures can equally well be used. Step
420 is to calculate tracker parameters TX, TY, RX, and RY. The
self-compensation procedure obtains these tracker parameters, among
others. Step 430 is to check whether the compensation procedure was
performed for the first time. If so, the compensation procedure is
performed a second time, and the parameter values are again calculated.
If not, step 440 is carried out to find a stability metric S. More
details on the method for calculating the stability metric S are given
hereinbelow. Step 450 is to check whether the termination criterion has
been met by the stability metric. If so, the tracker would be considered
stable and the method 400 ends. Following this, either tracker
compensation or commencement of measurements by the tracker begins. For
the particular exemplary embodiment discussed below, the stability metric
can vary from 0 to 1 (or 0 to 100%), with 0 indicating the least stable
tracker and 1 indicating the most stable tracker. As an example, a
termination criterion of 0.9 (or 90%) might be selected. The tracker
would then be considered stable if the stability metric were greater than
or equal to 0.9.

[0052] The stability metric S is calculated by performing the following
steps. The changes in the kinematic model parameters RX, RY, TX, TY are
calculated:

[0053] Here the subscript "new" refers to the parameters calculated in the
most recent measurement and the subscript "old" refers to the parameters
calculated in the measurement just before the most recent measurement.

[0054] Root-sum-squared (rss) values, ΔR, ΔT, are calculated
for the x and y components of the changes in the kinematic model
parameters:

[0059] The stability metric S is defined as the minimum value of the
stability ratio over the possible ranges of the tracker, which extend
from dmin to dmax:

S=Min(s(d)). (7)

[0060] As defined in equation (7), S is a dimensionless number that lies
on an interval [0, 1]. Immediately after the tracker 10 is powered on,
the temperature and the kinematic model parameters may change rapidly,
resulting in a relatively low value for S. Later, as the temperature
nears equilibrium and the model parameters change more slowly, S
approaches 1. The self-compensation cycle terminates when S exceeds the
specified tolerance. A typical tolerance would be 0.9. The method
described above need not be a linear function of A and B as given in
Equation (3) but could easily be generalized in other exemplary
embodiments. For example, if the manufacturer's performance specification
is a nonlinear function of range, one merely changes the formula equation
(3) above. An advantage of the embodiments of FIGS. 3 and 4 is that when
the automated warm-up has completed, the tracker 10 is not only warmed up
but also compensated. This method is particularly convenient if the
self-compensation method described hereinabove is used, since this
requires a minimum of user attention. The user need only run a quick test
to verify the accuracy of the instrument before taking measurements.

[0061] FIGS. 5-8 illustrate plots 500, 600, 700, 800 of the stability
metric versus number of self-compensation cycles to demonstrate the
method 400. FIGS. 5-7 illustrate trackers that were started from a cold
condition and FIG. 8 illustrates a tracker that was already thermally
equilibrated. FIGS. 5-8 illustrate that the warm-up time occurs over
approximately five compensation cycles (i.e., about 25 minutes). It is
appreciated that FIGS. 5-8 illustrate only examples and are illustrative
of the method 400. In other exemplary embodiments, other numbers of
compensation cycles are possible. FIGS. 5-8 therefore illustrate that as
thermal equilibrium approaches, the plots 500, 600, 700, 800 demonstrate
the plateau behavior as supported by the method 400.

[0062] In another exemplary embodiment, a self-test compensation method
performs the automated measurement and computes the parameters. The
targets are used for these measurements include a tracker mounted
retroreflector and a tracker mounted mirror. The algorithm evaluates the
termination criterion is called the sign change algorithm (SC). In SC,
when the parameter in question has stabilized, random oscillations in its
value start to become important relative to any systematic behavior due
to warm-up, which tends to be monotonic in nature. SC computes the delta
in each parameter from cycle to the next. Each time the delta changes
sign, a counter for the associate parameter is incremented. The loop is
terminated when each parameter has undergone N sign changes, where N is a
previously specified integer greater or equal to 1. N may be specified
either by the user or by the tracker manufacturer. The termination
criterion is effectively loosened or tightened by decreasing or
increasing N, respectively. An advantage of the SC embodiment is that
when the automated startup has completed, the tracker is not only warmed
up but also compensated, since it is based on the self-compensation
method.

[0063] An important aspect of the inventive methods described herein is to
minimize the time required to warm up the tracker. Thus far hereinabove,
the embodiments have mostly been directed toward methods for determining
when a tracker is warmed up. Now this application will consider in more
detail how warm-up time can be minimized. Trackers are equipped with
built-in heaters in the form of electric motors 32, 34. Tests have shown
that active heating by the use of electric motors can reduce warm-up time
significantly. For the most common situation, in which the tracker is
initially at ambient temperature, the warm-up time through the proper
application of motor heating may be reduced by a substantial amount. For
example, for one type of tracker, warm-up time is reduced by a factor of
four, from two hours to thirty minutes.

[0064] Besides a heat source, an accelerated warm-up process requires a
control mechanism. The control mechanism regulates the amount of
electrical current to be applied to the motors at any given time. An
optimized control mechanism applies current to the motors in such a way
as to minimize the warm-up time. In doing so it ensures that the required
quantity of heat is injected into the tracker. It also ensures that hot
spots, typically near the motors, are allowed to cool down and that cold
spots, typically at some distance from the motors, are allowed to warm
up. This process is called thermal relaxation. An effective method for
quickly obtaining thermal equilibrium throughout the body of a laser
tracker is to first provide a heating cycle followed by a thermal
relaxation cycle. Warm-up is not complete until both the heating process
and the thermal relaxation process have been completed. In general,
however, the heat may be effectively applied to a laser tracker in a
variety of temporal patterns, usually with higher levels of heat applied
more near the start of the warm-up procedure and lower levels of heat
applied near the end of the warm-up procedure.

[0065] In the ideal case, following warm-up the temperature at each point
within the tracker body remains, to a good approximation, constant over
time. In this case, the tracker is said to have reached thermal
equilibrium or, equivalently, to have equilibrated or to have reached a
temperature plateau.

[0066] After the tracker has reached thermal equilibrium, the motors
continue to be supplied with electrical current to carry out the
movements of the laser tracker structures during routine tracker
operation. Such movements require a relatively low level compared to the
application of full current to the tracker motors. For example, in
typical tracker operation of one type of tracker, the current usage is
about five percent of maximum current level.

[0067] In general, the warm-up procedure requires more time if the tracker
initially is relatively cold in comparison with ambient conditions and
less time if it is relatively warm. To minimize the warm-up time, the
control mechanism should take account of the initial tracker and air
temperatures and execute a warm-up sequence based on these temperatures.
The control mechanism should also ensure that the tracker is not damaged
by overheating the motors.

[0068] As will be appreciated by one skilled in the art, many different
types of control mechanisms are possible to specify the electrical
current in the motors at a given time. A simple approach would be to
apply a fixed amount of current to the motors for a fixed duration. This
approach is adequate for the most common situation, in which the tracker
is initially at or near ambient temperature. However, this approach may
overheat a tracker that is initially relatively warm and underheat a
tracker that is initially relatively cold.

[0069] Another type of control mechanism is real time proportional
control, which, as the name suggests, is based on real time measurements
of tracker and ambient air temperatures. With this type of control, a
particular set point for the tracker temperature is specified, and the
control mechanism increases or decreases the current to the motors in
proportion to the departure of the actual tracker temperature from the
set point. Real time proportional control approach does not provide the
shortest warm-up times because, for much of the time, the current sent to
the motors falls below the maximum value.

[0070] A related type of control mechanism is real time non-linear
control, which in general does not provide a warm-up time. This may be
inconvenient for tracker users, who want to know how long to wait before
starting to use their trackers.

[0071] Another type of control mechanism is based on a model-based
approach in which a mathematical model of the tracker is used to
determine how much current is applied to the motors as a function of
time. Such a model can be constructed from well-known results obtained
from the fields of thermodynamics and heat transfer.

[0072] In an exemplary model-based approach, the warm-up process consists
of a heating phase and a thermal relaxation phase. During the heating
phase, the maximum safe electrical current is applied to the motors for a
specific duration, which is calculated at the start. Then, during the
thermal relaxation phase, a lower current is applied to the motors as the
temperature distribution within the tracker relaxes to the equilibrium
state. The thermal relaxation time may also be calculated at the start.
Alternatively, a tracker test procedure, for example, a test procedure
using two-face measurements, as described hereinabove, may be performed
starting near the end of warm-up procedure to establish when the warm up
procedure should be terminated.

[0073] Description is now given of an exemplary embodiment based on a
thermal model that combines a heating model and a thermal relaxation
model. The heating model is obtained by treating the instrument as an
isothermal body having a mass m, average specific heat c, and heat
transfer coefficient relative to the surrounding air h. For the
instrument having a surface area a, the instrument in contact with air at
temperature Tair, the differential equation (8) gives the rate of
change of the instrument temperature T with time t:

dT/dt=-(ha/cm)T+{dot over (Q)}m/cm+{dot over
(Q)}ecm+(ha/cm)Tair. (8)

The first term on the right of the equation represents heat lost by the
instrument to the air. The second term represents the rate at which heat
is added to the instrument by the internal electronics ({dot over
(Q)}e) and the motors ({dot over (Q)}m), and the last term
represents heat transfer from the air to the instrument.

[0074] The quantity S is defined as the temperature of the tracker
relative to the ambient air temperature Tamb. The quantity Si
is defined as the initial tracker temperature relative to the ambient air
temperature Ti and the quantity Seq, is defined as the
equilibrium tracker temperature relative to the ambient air temperature.

S(t)=T(t)-Tamb, (9a)

Si(t)=Ti(t)-Tamb, (9b)

Seq(t)=Teq(t)-Tamb, (9c)

[0075] A solution of the differential equation can be written as equation
(9):

S(t)=Seq+(Si-Seq)e-t/τ, (10)

where the term Seq is a temperature difference the instrument
approaches asymptotically as time goes to infinity. This quantity depends
on quantities associated with material and environmental properties
within the Eq. (8). Ti is an initial (measured) temperature
difference of the instrument and τ is a heating time constant. It is
possible to determine the values of τ and Teq directly by
testing an instrument of a particular type. Testing has been carried out
to empirically verify that the Eq. (10) holds regardless of the ambient
temperature Tamb and the properties of the air such as specific heat
c and heat transfer coefficient h, which are usually difficult to
establish accurately. The testing method to determine the values τ
and Teq involves powering on an instrument of a given type, setting
the motor current to a desired fixed value, and iteratively measuring the
air temperature and the temperature of the instrument as the instrument
warms up. The test data is fit to the model of equation (9) by performing
a least squares fit calculation to find values for τ and Teq.

[0076] Equations (8) and (10) apply to both an initial heating phase in
which maximum current is applied to the tracker and a subsequent thermal
relaxation phase in which a lower current level is applied. This lower
current level is set to the current level applied to a motor during
normal operation of the tracker. The thermal equilibrium temperature
Teq depends on the current level applied to the motors and hence is
different for the heating phase and the thermal relaxation phase. For the
heating phase, the thermal equilibrium temperature is denoted
Teq=Teq1. For the thermal relaxation phase, the thermal
equilibrium temperature is denoted Teq=Teq2. In general, the
thermal equilibrium temperatures Teq1, Teq2 depend on the air
temperature and on the current level applied to the tracker.

[0077] The second part of the thermal model is the thermal relaxation
model, which is applicable during a secondary warm-up phase in which the
heat is allowed to diffuse among the internal tracker components as the
tracker approaches thermal equilibrium. Once thermal relaxation step is
complete, the instrument is properly warmed up and ready for use.

[0078] In an embodiment, the first structure 14 is called a yoke. The yoke
is symmetrical in appearance about a particular vertical plane. However,
the yoke is not symmetrical internally because a motor is mounted on one
side (the heated or hot side) of the yoke. The other side (the unheated
or cold side) of the yoke has no motor. A temperature S is defined with
respect to an ambient temperature: Sh=Th-Tamb,
Su=Tu-Tamb. In an embodiment, in thermal equilibrium,
there is a difference in temperature between the hot side and the cold
side. Equations (11) and (12) form the basis of the relaxation model:

m2c2{dot over (S)}h={dot over
(Q)}-h2a2Sh-k(Sh-Su), (11)

m2c2{dot over (S)}=h2a2Su+k(Sh-Su).
(12)

Here m2 is the mass of one side of the yoke, the two sides of the
yoke assumed to have the same mass; c2 is the average specific heat
capacity of the yoke; h2 is the heat transfer coefficient between
the air and the yoke; a2 is the effective surface area of the half
the yoke; k is an effective heat transfer constant between the hot side
and the cold side of the yoke; {dot over (Q)} is the rate of heat
transfer from the hot side to the cold side of the yoke; Th is the
temperature of the hot (heated) side; and Tu is the temperature of
the cold (unheated) side. The equations (11) and (12) are basically
reformatted versions of equation (8) but written specifically for the hot
and cold sides of the yoke.

[0079] If equation (12) is subtracted from equation (11) and the resulting
equation is simplified using the temperature difference
α=Th-Tu=Sh-Su, equation (13) is obtained:

m2c2{dot over (α)}={dot over
(Q)}-(h2α2+2k)α. (13)

Equation 10 is a differential equation whose solution after
simplification is

α(t)=αeq+(αi-αeq)e-t/σ-
. (14)

Here α is equal to the hot side temperature minus the cold side
temperature at a particular time t, αeq is the temperature
difference at thermal equilibrium (as time approaches infinity),
αi is the (measured) temperature difference at the start of
the thermal relaxation phase, which corresponds to the end of the heating
phase, and σ is a thermal relaxation time constant. Experimental
data is used to find the values of the relaxation time constant σ
and the equilibrium temperature difference αeq.

[0080] Equation (10) is solved algebraically to find the prescribed
heating time theat to reach a particular temperature T during the
heating phase. The result is shown in equation (15). Equation (14) is
solved algebraically to find the prescribed relaxation time trelax
to reach a particular temperature difference α=Th-Tu. The
result is shown in equation (16).

theat=τ log((Ti-Teq)/(T-Teq)), (15)

trelax=σ
log((αi-αeq)/(α-αeq)). (16)

Here theat is the required heating time to reach a given temperature
T during a heating phase, and trelax is the required thermal
relaxation time for the two sides of the yoke to reach a given
temperature difference α during a relaxation phase. A particular
value of temperature T is selected as the transition temperature
Ttrans between the heating phase and the thermal relaxation phase.
Experiments may be carried out to find the value T=Ttrans that
minimize the total warmup time ttotal=theat+twarmup for a
given acceptable temperature difference α=Th-Tu. In the
discussion above, the equations (10) and (14) were obtained from heat
transfer equations. FIG. 11 is a plot that compares curves based on
equation (10) to temperatures observed in a particular model laser
tracker during a heating phase for a given applied current level. In the
plot 1100, the dashed line 1105 is the actual test data and the solid
line 1107 is the model prediction using the model parameters obtained by
fitting the experimental data to the equation (10). FIG. 12 is a plot
that compares curves based on equation (14) to temperatures observed in a
particular model laser tracker during a relaxation phase for a given
applied current level. In the plot 1200, the dashed line 1205 is the
actual test data and the solid line 1207 is the model prediction using
the model parameters obtained by fitting the experimental data to the
equation (14). These plots show that the warm-up behavior of the tracker
matches the predicted behavior relatively well. For the experimental data
shown in FIG. 11, the temperature T was found by averaging the readings
of four temperature sensors in the yoke (first structure 14) of the
tracker, two temperature sensors on the hot side and two temperature
sensors on the cold side. The temperature sensors may be attached to
processors, for example, processor 925 in FIG. 9. For the experimental
data shown in FIG. 12, the temperature difference α is found by
subtracting the average of the readings of two temperature sensors on the
cold side from the average of the readings of two temperature sensors on
the hot side.

[0081] In an embodiment, the temperature sensors in the yoke (the first
structure 14) are used to find the temperatures Ti, Th, and
Tu in the equations above. One reason for using the temperature
sensors in the yoke is that the yoke is close to the payload and hence
may have a relatively significant influence on the thermal distribution
within the payload. The payload in some types of trackers contains
optical and opto-mechanical components that are relatively sensitive to
thermal effects. In tests on a particular type of tracker, warm-up times
calculated from temperatures measured by sensors in the yoke were found
to correlate well to good tracker performance, as evaluated by performing
two-face tests. In other types of trackers, it may be important to
consider the temperatures measured within the second structure 15, which
might be a payload or a mirror assembly (including a zenith motor). In
other cases, it may be important to consider temperatures measured by
temperature sensors in the base 16. As heat is initially applied to the
base, the gimbal point 22 expands upward. To ensure that the gimbal point
has reached a stable position, it may be important to use temperatures
from the temperature sensors in the base 16, as well as in the first
structure 14 and the second structure 15. In general, the importance of
temperature sensors located at different positions on or in the tracker
depends on the type of tracker.

[0082] As explained hereinabove, tests are run to determine parameter
values. The parameters extracted from the fitting of experimental data to
the exponential curves of equations (10) and (14) may include a heating
time constant τ, a relaxation time constant σ, an equilibrium
value Teq1 for an internal tracker temperature given an application
of maximum motor current, an equilibrium value Teq2 for an internal
tracker temperature given an application of reduced motor current, and an
equilibrium value αeq for a temperature difference given an
application of a reduced motor current. The equilibrium temperatures
Teq1, Teq2, αeq depend on ambient air temperature as
well as current levels applied to the motors. It may be important to
perform measurements to determine how the equilibrium temperatures depend
on the ambient air temperature. The equilibrium values Teq1,
Teq2 may be temperatures approached asymptotically at a particular
location in or on the tracker or it may be based on a collection of
temperatures--for example, on an average of readings of four temperature
sensors within the second structure 14. Similarly, the equilibrium value
αeq may be the temperature difference approached
asymptotically between readings of two temperature sensors at particular
locations in or on the tracker, or they may be based on a collection of
temperatures--for example, the difference between the average of readings
of two temperature sensors on one side and two temperature sensors on the
other side of the second structure 14. Tests may also be carried out to
determine a transition temperature T=Ttrans that minimizes the total
warmup time ttotal=theat+twarmup.

[0083] In one of the embodiment described hereinabove, a constant maximum
current is applied during a first phase (heating phase) and a constant
reduced current is applied during a second phase (thermal relaxation
phase). The constant reduced current is set to approximately the level of
the operating current of the tracker in normal operation. The current may
be applied in a variety of different temporal patterns. The pattern of
current as a function of time (the temporal pattern) is called a profile.
If the tracker has a first motor and a second motor, a first profile is
applied to the first motor and a second profile is applied to the second
motor.

[0084] One type of motor 32, 34 is a brushless motor. For such a motor,
current may be engaged to turn a shaft or to simply heat up to motor and
its surroundings without turning a shaft. In other words, the first motor
32 and the second motor 34 may be heated through the application of
current without turning the first structure 14 or the second structure
15. This may be advantageous as it eliminates unnecessary movement of the
structures; however, the warm-up procedures described herein may be
applied with or without the movement of the first structure and the
second structure.

[0085] To minimize wasted time, a notification can be given to the tracker
operator that the tracker is warmed up. This notification may take many
forms. For example, lights can flash or sounds can be made to indicate
that the tracker is warmed up. In addition, a computer screen may show a
countdown message that indicates the time remaining until warm-up is
completed. Other methods of notifying the operator can be used. Without
the invention described herein, the operator may tend to overestimate the
time required for the tracker to warm up. As a result, the operator may
waste time in waiting for warm-up to be completed.

[0086] The methods for minimizing warm-up time described hereinabove have
been directed toward to use of motor heating through the application of
current. It is also possible to heat the tracker using other heating
devices such as thermal blankets. Thermal blankets may be wrapped around
major tracker elements, for example, to speed the warm-up process. The
use of such heater blankets or other heating devices to warm the tracker
generally should not be confused with the use of heater blankets to
stabilize lasers. It is common practice in laser trackers to wrap a
heater blanket around a helium-neon (HeNe) laser tube used as a source
for interferometry measurements in order to stabilize the laser modes
emitted by the HeNe laser. The purpose of such heater blankets is to
stabilize the laser and such blankets cannot be used effectively to
independently adjust the temperature of the tracker structure.

[0087] An exemplary method 1300 for warming up a laser tracker is shown in
FIG. 13. Step 1310 is to provide an instrument that includes a first
structure 14 rotatable about a first axis 20 with respect to the base 16,
a first motor 32 capable of rotating the first structure 14 about the
first axis 20, a second structure 15 rotatable about a second axis 18
with respect to the first structure 14, and a second motor 34 capable of
rotating the second structure 14 about the second axis 18. As explained
hereinabove, the first structure and second structure may have a
different form than that shown in FIG. 1. For example, the second
structure may be a rotatable mirror attached to a shaft onto which are
mounted a pair of bearings, a motor, and an angle transducer such as an
angular encoder.

[0088] Step 1320 is to determine a first temperature, the first
temperature being a temperature of the air in which the instrument sits.
One way to determine such a temperature is to measure the air temperature
(sometimes called the ambient temperature) with an air temperature
sensor. Another way to determine a first temperature is to estimate it,
for example, based on a typical reading within a factory or on a setting
of a remote thermostat.

[0089] Step 1330 is to determine a second temperature, the second
temperature being a temperature of the instrument. One way to determine
such a temperature is to measure, at an initial time, one or more
temperatures of the instrument, the temperatures referring generally to
temperatures on or in the instrument. If the second temperature is based
on the reading of a single temperature sensor, then the second
temperature corresponds to the location of the temperature sensor in or
on the instrument. If the second temperature is based on the readings of
more than one temperature sensor, then the second temperature may be
based on a collection of measured temperatures. For example, if four
temperature sensors are disposed internally in an instrument, the second
temperature may be the average of the four temperature sensors. Another
way to determine a second temperature is to estimate it. For example, if
the instrument has been at a stable room temperature for an extended
period and, if the instrument is turned on at the start of the warm-up
procedure, the instrument may reasonably be assumed to be at the air
temperature.

[0090] Step 1340 is to determine a third temperature, the third
temperature being a predicted temperature of the instrument in a warmed
up condition. The third temperature is the temperature approached
asymptotically by the instrument as it operates at reduced currents
representative of the currents applied to the first and second motors
during normal operation of the instrument. In the discussion hereinabove,
this equilibrium temperature is denoted as Teq2. In general, this
temperature is a function of both the ambient air temperature and the
typical average current applied to the tracker in normal operation.

[0091] Step 1350 is to determine a first profile, wherein the first
profile is an electrical current to be applied to the first motor, the
electrical current varying as a function of time according to a rule
based at least in part on the first temperature, the second temperature,
and the third temperature. The term profile refers to a temporal pattern
in the application of motor current. In one of the embodiments above, the
profile included the application of a maximum current for a prescribed
heating time theat followed by the application of a reduced current
for a different prescribed time twarmup. In this case, the duration
of the overall warmup procedure is established ahead of time based on an
allowable temperature difference α=Th-Tu selected in
equation (16). In another embodiment, the time twarmup is not
precisely established ahead of time but is based on the results of
accuracy checks carried out by the instrument.

[0092] Step 1360 is to determine a second profile, wherein the second
profile is an electrical current to be applied to the second motor, the
electrical current varying as a function of time according to a rule
based at least in part on the first temperature, the second temperature,
and the third temperature. This step is like step 1350 except that the
electrical current is applied to the second motor rather than to the
first motor.

[0093] Step 1370 is to apply the first and second profiles. In other
words, the current profiles determined in steps 1350, 1360 are applied to
the motors.

[0094] The methods described above may be implemented manually or with the
aid of a computing system located either internal to the tracker or in an
external computer system attached to the tracker. Methods based on the
use of a computing system, either internal or external to the tracker,
are advantageous because they save operator time.

[0095] An exemplary computing system (processing system) 900 is shown in
FIG. 9. Processing system 900 comprises tracker processing unit 910 and
optionally computer 980. Processing unit 910 includes at least one
processor, which may be a microprocessor, digital signal processor (DSP),
field programmable gate array (FPGA), or similar device. Processing
capability is provided to process information and issue commands to
internal tracker processors. Such processors may include position
detector processor 912, azimuth encoder processor 914, zenith encoder
processor 916, indicator lights processor 918, absolute distance meter
(ADM) processor 926, interferometer (IFM) processor 922, camera processor
924, temperature sensor processor 925, azimuth motor processor 932, and
zenith motor processor 934. Auxiliary unit processor 970 optionally
provides timing and microprocessor support for other processors within
tracker processor unit 910. Preferably, auxiliary unit processor 970
communicates with other processors by means of device bus 930, which may
transfer information throughout the tracker by means of data packets, as
is well known in the art. Computing capability may be distributed
throughout tracker processing unit 910, with DSPs and FPGAs performing
intermediate calculations on data collected by tracker sensors. The
results of these intermediate calculations are returned to auxiliary unit
processor 970. Auxiliary unit 970 may be attached to the main body of
laser tracker 10 through a long cable, or it may be pulled within the
main body of the laser tracker so that the tracker attaches directly (and
optionally) to computer 980. Auxiliary unit 970 may be connected to
computer 980 by connection 940, which is preferably an Ethernet cable or
wireless connection. Auxiliary unit 970 and computer 980 may be connected
to the network through connections 942, 944, which may be Ethernet cables
or wireless connections. Stability computations as described in the
exemplary embodiments herein may use processors (microprocessors, DSPs,
or FPGAs) from within processing unit 900 or by optional computer 980.

[0096] As will be appreciated by one skilled in the art, aspects of the
present invention may be embodied as a system, method or computer program
product. Accordingly, aspects of the present invention may take the form
of an entirely hardware embodiment, an entirely software embodiment
(including firmware, resident software, micro-code, etc.) or an
embodiment combining software and hardware aspects that may all generally
be referred to herein as a "circuit," "module" or "system." Furthermore,
aspects of the present invention may take the form of a computer program
product embodied in one or more computer readable medium(s) having
computer readable program code embodied thereon.

[0097] Any combination of one or more computer readable medium(s) may be
utilized. The computer readable medium may be a computer readable signal
medium or a computer readable storage medium. A computer readable storage
medium may be, for example, but not limited to, an electronic, magnetic,
optical, electromagnetic, infrared, or semiconductor system, apparatus,
or device, or any suitable combination of the foregoing. More specific
examples (a non-exhaustive list) of the computer readable storage medium
would include the following: an electrical connection having one or more
wires, a portable computer diskette, a hard disk, a random access memory
(RAM), a read-only memory (ROM), an erasable programmable read-only
memory (EPROM or Flash memory), an optical fiber, a portable compact disc
read-only memory (CD-ROM), an optical storage device, a magnetic storage
device, or any suitable combination of the foregoing. In the context of
this document, a computer readable storage medium may be any tangible
medium that can contain, or store a program for use by or in connection
with an instruction execution system, apparatus, or device.

[0098] A computer readable signal medium may include a propagated data
signal with computer readable program code embodied therein, for example,
in baseband or as part of a carrier wave. Such a propagated signal may
take any of a variety of forms, including, but not limited to,
electro-magnetic, optical, or any suitable combination thereof. A
computer readable signal medium may be any computer readable medium that
is not a computer readable storage medium and that can communicate,
propagate, or transport a program for use by or in connection with an
instruction execution system, apparatus, or device.

[0099] Program code embodied on a computer readable medium may be
transmitted using any appropriate medium, including but not limited to
wireless, wireline, optical fiber cable, RF, etc., or any suitable
combination of the foregoing.

[0100] Computer program code for carrying out operations for aspects of
the present invention may be written in any combination of one or more
programming languages, including an object oriented programming language
such as Java, Smalltalk, C++ or the like and conventional procedural
programming languages, such as the "C" programming language or similar
programming languages. The program code may execute entirely on the
user's computer, partly on the user's computer, as a stand-alone software
package, partly on the user's computer and partly on a remote computer or
entirely on the remote computer or server. In the latter scenario, the
remote computer may be connected to the user's computer through any type
of network, including a local area network (LAN) or a wide area network
(WAN), or the connection may be made to an external computer (for
example, through the Internet using an Internet Service Provider).

[0101] Aspects of the present invention are described below with reference
to flowchart illustrations and/or block diagrams of methods, apparatus
(systems) and computer program products according to embodiments of the
invention. It will be understood that each block of the flowchart
illustrations and/or block diagrams, and combinations of blocks in the
flowchart illustrations and/or block diagrams, can be implemented by
computer program instructions. These computer program instructions may be
provided to a processor of a general purpose computer, special purpose
computer, or other programmable data processing apparatus to produce a
machine, such that the instructions, which execute via the processor of
the computer or other programmable data processing apparatus, create
means for implementing the functions/acts specified in the flowchart
and/or block diagram block or blocks.

[0102] These computer program instructions may also be stored in a
computer readable medium that can direct a computer, other programmable
data processing apparatus, or other devices to function in a particular
manner, such that the instructions stored in the computer readable medium
produce an article of manufacture including instructions which implement
the function/act specified in the flowchart and/or block diagram block or
blocks.

[0103] The computer program instructions may also be loaded onto a
computer, other programmable data processing apparatus, or other devices
to cause a series of operational steps to be performed on the computer,
other programmable apparatus or other devices to produce a computer
implemented process such that the instructions which execute on the
computer or other programmable apparatus provide processes for
implementing the functions/acts specified in the flowchart and/or block
diagram block or blocks.

[0104] The flowchart and block diagrams in the Figures illustrate the
architecture, functionality, and operation of possible implementations of
systems, methods and computer program products according to various
embodiments of the present invention. In this regard, each block in the
flowchart or block diagrams may represent a module, segment, or portion
of code, which comprises one or more executable instructions for
implementing the specified logical function(s). It should also be noted
that, in some alternative implementations, the functions noted in the
block may occur out of the order noted in the figures. For example, two
blocks shown in succession may, in fact, be executed substantially
concurrently, or the blocks may sometimes be executed in the reverse
order, depending upon the functionality involved. It will also be noted
that each block of the block diagrams and/or flowchart illustration, and
combinations of blocks in the block diagrams and/or flowchart
illustration, can be implemented by special purpose hardware-based
systems that perform the specified functions or acts, or combinations of
special purpose hardware and computer instructions.

[0105] In exemplary embodiments, where the automated warm-up methods are
implemented in hardware, the automated warm-up methods described herein
can be implemented with any or a combination of the following
technologies, which are each well known in the art: a discrete logic
circuit(s) having logic gates for implementing logic functions upon data
signals, an application specific integrated circuit (ASIC) having
appropriate combinational logic gates, a programmable gate array(s)
(PGA), FPGAs, DSPs, etc.

[0106] While the description above refers to particular embodiments of the
present invention, it will be understood that many modifications may be
made without departing from the spirit thereof. The accompanying claims
are intended to cover such modifications as would fall within the true
scope and spirit of the present invention.

[0107] The presently disclosed embodiments are therefore to be considered
in all respects as illustrative and not restrictive, the scope of the
invention being indicated by the appended claims, rather than the
foregoing description, and all changes which come within the meaning and
range of equivalency of the claims are therefore intended to be embraced
therein.